# Uniform line fillings.

@article{Marakis2019UniformLF, title={Uniform line fillings.}, author={Evangelos Marakis and Matthias Christiaan Velsink and Lars J Corbijn van Willenswaard and R. Uppu and Pepijn W. H. Pinkse}, journal={Physical review. E}, year={2019}, volume={99 4-1}, pages={ 043309 } }

Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls, and arbitrary-dimensional hyperballs… CONTINUE READING

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